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%I #18 Mar 03 2020 08:50:44
%S 1,2,5,36,54,441,473,6525,52577,124025,683820,1513754,1920552,6079931,
%T 6762923,14751657,17052782,17310942,36543714,49919939,60260967,
%U 251849052,364535720,372476909,562047389,670395564,670440852,783856979,824626800,1084201689,1122603809
%N Numbers k such that the sum of divisors of k (A000203) and the sum of proper divisors of k (A001065) are both triangular numbers (A000217).
%C Are 1 and 36 the only terms that are also triangular numbers?
%C No other triangular terms up to A000217(10^8). - _Michel Marcus_, Mar 01 2020
%H Amiram Eldar, <a href="/A329704/b329704.txt">Table of n, a(n) for n = 1..48</a>
%e 5 is a term since sigma(5) = 6 and sigma(5) - 5 = 1 are both triangular numbers.
%t triQ[n_] := IntegerQ @ Sqrt[8*n+1]; Select[Range[10^5], triQ[(s = DivisorSigma[1, #])] && triQ[s - #] &]
%o (PARI) isok(k) = my(s=sigma(k)); ispolygonal(s, 3) && ispolygonal(s-k, 3); \\ _Michel Marcus_, Feb 29 2020
%Y Intersection of A045745 and A045746.
%Y Cf. A000203, A000217, A001065.
%K nonn
%O 1,2
%A _Amiram Eldar_, Feb 28 2020